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Math Help - Differences of sets

  1. #1
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    Differences of sets

    If the difference of sets A and B is the set containing elements that are in A but not in B and B is an all-inclusive set then is A-B={null set} or just A-B=null set?

    I was thinking that it would be A-B={null set} since the definition of the difference of sets is that it is, "the set containing..."

    Thanks!
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  2. #2
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    Quote Originally Posted by buddyp450 View Post
    If the difference of sets A and B is the set containing elements that are in A but not in B and B is an all-inclusive set then is A-B={null set} or just A-B=null set?
    I was thinking that it would be A-B={null set} since the definition of the difference of sets is that it is, "the set containing..."
    I, for one, have no idea what you point is. What are you asking?
    Here is a fact: A \subseteq B\quad  \Leftrightarrow \quad A\backslash B = \emptyset  .
    Last edited by Plato; February 22nd 2010 at 06:25 AM. Reason: typo
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  3. #3
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    I'm sorry, let me try to be more clear as I'm new to discrete mathematics.

    A = {1, 2, 3, 4, 5}
    B = {1, 2, 3, 4, 5}

    so does

    A-B = \emptyset

    or

    A-B = { \emptyset}

    and could you please explain why?
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  4. #4
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    Notation

    Quote Originally Posted by buddyp450 View Post
    I'm sorry, let me try to be more clear as I'm new to discrete mathematics.

    A = {1, 2, 3, 4, 5}
    B = {1, 2, 3, 4, 5}

    so does

    A-B = \emptyset

    or

    A-B = { \emptyset}

    and could you please explain why?
    \emptyset is equivalent to {}. This is standard notation. E.g., { \emptyset} is the set containing the empty set. So, A-B is \emptyset or {}, not { \emptyset}.
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  5. #5
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Plato View Post
    I, for one, have no idea what you point is. What are you asking?
    Here is a fact: A \subseteq B\quad  \Leftrightarrow \quad B\backslash A = \emptyset  .
    Is that a typo, or am I misunderstanding the notation? \{1\}\subset\{1,2\} but \{1,2\}-\{1\}=\{2\}
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  6. #6
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    I think that by "B is an all inclusive set" you mean that B is the universal set. In that case, everything is in B so "are in A but not in B" does not apply to anything since there is nothing that is "not in B". A- B is the empty set.
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